-5(z-8)(-z+3)=0

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Solution for -5(z-8)(-z+3)=0 equation: 


Simplifying
-5(z + -8)(-1z + 3) = 0

Reorder the terms:
-5(-8 + z)(-1z + 3) = 0

Reorder the terms:
-5(-8 + z)(3 + -1z) = 0

Multiply (-8 + z) * (3 + -1z)
-5(-8(3 + -1z) + z(3 + -1z)) = 0
-5((3 * -8 + -1z * -8) + z(3 + -1z)) = 0
-5((-24 + 8z) + z(3 + -1z)) = 0
-5(-24 + 8z + (3 * z + -1z * z)) = 0
-5(-24 + 8z + (3z + -1z2)) = 0

Combine like terms: 8z + 3z = 11z
-5(-24 + 11z + -1z2) = 0
(-24 * -5 + 11z * -5 + -1z2 * -5) = 0
(120 + -55z + 5z2) = 0

Solving
120 + -55z + 5z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + -11z + z2) = 0

Factor a trinomial.
5((3 + -1z)(8 + -1z)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3

Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8
Solution
z = {3, 8}

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